vetorial

Vetorial is an adjective used to describe concepts related to vectors and vector spaces. In mathematics, vectors are objects that have both magnitude and direction and live in a vector space. A vetorial quantity is often represented by a vector, typically expressed in coordinates relative to a basis. In many languages, such as Portuguese and Spanish, the term vetorial denotes relation to vectors.

Vetorial concepts include vector-valued functions, which map a domain to a vector space, and vector fields, which assign a vector to every point in a space. Vector operations such as addition and scalar multiplication follow linear algebra rules. Vector calculus studies properties of vector fields using differential operators such as gradient, divergence, and curl.

In physics and engineering, vectorial quantities describe magnitude and direction, including velocity, force, and momentum. In computer graphics and vision, vetorial representations underlie shading, normals, and transformations. Matrix representations encode linear transformations acting on vectors; change of basis provides coordinate-free descriptions.

The term is often contrasted with scalar quantities and with tensor objects in broader contexts; however, vectors can be components of tensors. Related concepts include vector, vector space, linear transformation, vector field, gradient, divergence, and curl.